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Simplifying x = 0.6x2 + -3x + -1.5 Reorder the terms: x = -1.5 + -3x + 0.6x2 Solving x = -1.5 + -3x + 0.6x2 Solving for variable 'x'. Reorder the terms: 1.5 + x + 3x + -0.6x2 = -1.5 + -3x + 0.6x2 + 1.5 + 3x + -0.6x2 Combine like terms: x + 3x = 4x 1.5 + 4x + -0.6x2 = -1.5 + -3x + 0.6x2 + 1.5 + 3x + -0.6x2 Reorder the terms: 1.5 + 4x + -0.6x2 = -1.5 + 1.5 + -3x + 3x + 0.6x2 + -0.6x2 Combine like terms: -1.5 + 1.5 = 0.0 1.5 + 4x + -0.6x2 = 0.0 + -3x + 3x + 0.6x2 + -0.6x2 1.5 + 4x + -0.6x2 = -3x + 3x + 0.6x2 + -0.6x2 Combine like terms: -3x + 3x = 0 1.5 + 4x + -0.6x2 = 0 + 0.6x2 + -0.6x2 1.5 + 4x + -0.6x2 = 0.6x2 + -0.6x2 Combine like terms: 0.6x2 + -0.6x2 = 0.0 1.5 + 4x + -0.6x2 = 0.0 Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -2.5 + -6.666666667x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -6.666666667x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -6.666666667x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -6.666666667x + x2 = 0 + 2.5 -6.666666667x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -6.666666667x + x2 = 2.5 The x term is -6.666666667x. Take half its coefficient (-3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. -6.666666667x + 11.11111112 + x2 = 2.5 + 11.11111112 Reorder the terms: 11.11111112 + -6.666666667x + x2 = 2.5 + 11.11111112 Combine like terms: 2.5 + 11.11111112 = 13.61111112 11.11111112 + -6.666666667x + x2 = 13.61111112 Factor a perfect square on the left side: (x + -3.333333334)(x + -3.333333334) = 13.61111112 Calculate the square root of the right side: 3.689323938 Break this problem into two subproblems by setting (x + -3.333333334) equal to 3.689323938 and -3.689323938.Subproblem 1
x + -3.333333334 = 3.689323938 Simplifying x + -3.333333334 = 3.689323938 Reorder the terms: -3.333333334 + x = 3.689323938 Solving -3.333333334 + x = 3.689323938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = 3.689323938 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = 3.689323938 + 3.333333334 x = 3.689323938 + 3.333333334 Combine like terms: 3.689323938 + 3.333333334 = 7.022657272 x = 7.022657272 Simplifying x = 7.022657272Subproblem 2
x + -3.333333334 = -3.689323938 Simplifying x + -3.333333334 = -3.689323938 Reorder the terms: -3.333333334 + x = -3.689323938 Solving -3.333333334 + x = -3.689323938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.333333334' to each side of the equation. -3.333333334 + 3.333333334 + x = -3.689323938 + 3.333333334 Combine like terms: -3.333333334 + 3.333333334 = 0.000000000 0.000000000 + x = -3.689323938 + 3.333333334 x = -3.689323938 + 3.333333334 Combine like terms: -3.689323938 + 3.333333334 = -0.355990604 x = -0.355990604 Simplifying x = -0.355990604Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.022657272, -0.355990604}
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